Séries Temporais: Estimação da série diária de ação GOOG
Adriano Marcos Rodrigues Figueiredo, e-mail: adriano.figueiredo@ufms.br
19 abril 2023
Abstract
This is an undergrad student level instruction for class use. The reader is encouraged to enhance the model changing the train data.Licença
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.
License: CC BY-SA 4.0
Citação
Sugestão de citação: FIGUEIREDO, Adriano Marcos Rodrigues. Séries Temporais: Estimação da série diária de ação GOOG. Campo Grande-MS,Brasil: RStudio/Rpubs, 2023. Disponível em <http://rpubs.com/amrofi/fable_GOOG_daily>.
1 Dados para exemplo
Neste exercício, usarei a série de preços da ação da Alphabet Inc. (GOOG).
Vou chamar os dados por uma função derivada do quantmod que está no
tidyquant, tq_get. Veja que ele vem em tibble. Então
geramos o tsibble. Depois preenchemos os gaps implicitos
com o fill_gaps.
library(tidyquant)
x.tbl <- tq_get("GOOG")
# XTS PARA TSIBBLE
library(tsibble)
library(tsibbledata)
library(magrittr)
library(dplyr)
x_tbl_ts <- as_tsibble(x.tbl)
head(x_tbl_ts)fabletools::autoplot(x_tbl_ts, close)
# fill gaps com ultimo valor ----------
library(tidyr)
dados.full2 <- x_tbl_ts[-1] %>%
tsibble::fill_gaps() %>%
tidyr::fill(c(open, high, low, close, volume, adjusted), .direction = "down")
print(dados.full2)# A tsibble: 3,759 x 7 [1D]
date open high low close volume adjusted
<date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 2013-01-02 17.9 18.1 17.8 18.0 102033017 18.0
2 2013-01-03 18.1 18.2 18.0 18.0 93075567 18.0
3 2013-01-04 18.2 18.5 18.1 18.4 110954331 18.4
4 2013-01-05 18.2 18.5 18.1 18.4 110954331 18.4
5 2013-01-06 18.2 18.5 18.1 18.4 110954331 18.4
6 2013-01-07 18.3 18.4 18.2 18.3 66476239 18.3
7 2013-01-08 18.3 18.3 18.0 18.3 67295297 18.3
8 2013-01-09 18.2 18.4 18.1 18.4 81291563 18.4
9 2013-01-10 18.5 18.6 18.3 18.5 73703226 18.5
10 2013-01-11 18.5 18.5 18.3 18.4 51600690 18.4
# ℹ 3,749 more rowsO gráfico para o preço de fechamento (close) será:
fabletools::autoplot(dados.full2, close)
O leitor pode testar agora as ferramentas de forecast do fable e fabletools.
library(fpp3)
fit <- dados.full2 %>%
model(arima = ARIMA(close), ets = ETS(close), theta = THETA(close))
fit_fc <- fit %>%
forecast(h = 365)
fit_fc %>%
autoplot(dados.full2, level = NULL) + labs(y = "valor de X", title = "Exemplo de forecast após fill_gaps")
2 Usando o pacote
prophet
Agora farei um ajuste com o Facebook Prophet:
# Prophet model ------------------ seguindo
# https://rpubs.com/amrofi/prophet_bitcoin
library(prophet)
library(tidyverse)
dados.ph <- dados.full2[, c(1, 5)] # peguei apenas a date e a close
colnames(dados.ph) <- c("ds", "y") # o prophet requer esses nomes de colunas
Model1 <- prophet(dados.ph, daily.seasonality = TRUE)
class(Model1) # objeto do prophet[1] "prophet" "list" ## Criar dataframe com mais 365 obs a frente (fora da amostra) ---------
Future1 <- make_future_dataframe(Model1, periods = 365)
tail(Future1)## Previsao pelo Model1 para as datas de Future1 ------------
Forecast1 <- predict(Model1, Future1)
class(Forecast1)[1] "data.frame"## gráficos do forecast -------------
dyplot.prophet(Model1, Forecast1)Fica a dica para o leitor avaliar a presença de efeitos ARCH.
3 Usando o pacote
fable.prophet com split
Neste caso, conforme Hyndman e Athanasopoulos (2020), capítulo 12.2, o modelo Facebook (TAYLOR e LETHAM, 2018) é útil para estimar séries diárias, e principalmente aquelas com sazonalidades semanal e anual, além de efeitos de feriados. Ele pode ser considerado um modelo de regressão não linear da forma:
\[ y_t = g(t) + s(t) + h(t) + \varepsilon_t, \]
em que \(g(t)\) descreve a tendência linear (ou “termo de crescimento”), \(s(t)\) descreve os vários padrões sazonais, \(h(t)\) captura os efeitos do feriado, e \(\varepsilon_t\) é um termo de erro de ruído branco. A tendência linear é selecionada automaticamente se não for especificada explicitamente. O componente sazonal consiste em termos de Fourier dos períodos relevantes. Por padrão, a ordem 10 é usada para sazonalidade anual e a ordem 3 é usada para sazonalidade semanal, conforme Hyndman e Athanasopoulos (2020, tradução livre). Os efeitos de feriado são adicionados como variáveis dummies simples. O modelo é estimado usando uma abordagem bayesiana para permitir a seleção automática dos pontos de mudança e outras características do modelo.
Estimaremos juntamente aos modelos ARIMA,
ETS, THETA anteriormente estimados, dentro do
ambiente fable e fable.prophet. Farei a regra
80-20 para amostras treino (3806*0.80 = 3044 dias = “2019-05-04”) e
teste (3806-3044 = 762 dias = após “2019-05-05”), obtido a partir do
dataset completo para os gaps implicitos.
library(fable.prophet)
library(fable)
train <- dados.full2 %>%
filter_index(~"2021-03-26") # 2591*0.80 = 2073 2021-03-26
h = length(dados.full2$close) - length(train$close)
h[1] 753fit.all <- train %>%
model(arima = ARIMA(close, stepwise = FALSE, approximation = FALSE), ets = ETS(close),
theta = THETA(close), prophet = prophet(close ~ growth("linear") + season(period = "day",
order = 10) + season(period = "week", order = 5) + season(period = "year",
order = 3))) %>%
mutate(combination = (ets + arima + theta + prophet)/4)fitall_fc <- fit.all %>%
forecast(h = h)
fitall_fc %>%
autoplot(dados.full2, level = NULL) + labs(y = "valor da ação", title = "Forecast com ARIMA, ETS, THETA e FABLE.PROPHET, para GOOG")
fc_accuracy <- fitall_fc %>%
accuracy(dados.full2)
# acurácia ordenada pelo RMSE
fc_accuracy %>%
group_by(.model) %>%
summarise(RMSE = mean(RMSE), MAE = mean(MAE), MASE = mean(MASE)) %>%
arrange(RMSE)Forecasts:
library(fable)
library(fable.prophet)
fitall_fc2 <- fit.all %>%
forecast(h = h + 60)
fitall_fc2 %>%
autoplot(dados.full2, level = c(95)) + labs(y = "valor da ação", title = "Forecast com ARIMA, ETS, THETA e FABLE.PROPHET, para o GOOG")
Representarei apenas os forecasts do período de “2023-01-01” a “2023-06-17” para não ficar muito extenso.
fitall_fc2 %>%
filter_index("2023-01-01" ~ "2023-06-17") %>%
knitr::kable()| .model | date | close | .mean |
|---|---|---|---|
| arima | 2023-01-01 | N(102, 262) | 101.9362 |
| arima | 2023-01-02 | N(102, 263) | 101.9362 |
| arima | 2023-01-03 | N(102, 263) | 101.9362 |
| arima | 2023-01-04 | N(102, 264) | 101.9362 |
| arima | 2023-01-05 | N(102, 264) | 101.9362 |
| arima | 2023-01-06 | N(102, 264) | 101.9362 |
| arima | 2023-01-07 | N(102, 265) | 101.9362 |
| arima | 2023-01-08 | N(102, 265) | 101.9362 |
| arima | 2023-01-09 | N(102, 266) | 101.9362 |
| arima | 2023-01-10 | N(102, 266) | 101.9362 |
| arima | 2023-01-11 | N(102, 266) | 101.9362 |
| arima | 2023-01-12 | N(102, 267) | 101.9362 |
| arima | 2023-01-13 | N(102, 267) | 101.9362 |
| arima | 2023-01-14 | N(102, 268) | 101.9362 |
| arima | 2023-01-15 | N(102, 268) | 101.9362 |
| arima | 2023-01-16 | N(102, 268) | 101.9362 |
| arima | 2023-01-17 | N(102, 269) | 101.9362 |
| arima | 2023-01-18 | N(102, 269) | 101.9362 |
| arima | 2023-01-19 | N(102, 270) | 101.9362 |
| arima | 2023-01-20 | N(102, 270) | 101.9362 |
| arima | 2023-01-21 | N(102, 270) | 101.9362 |
| arima | 2023-01-22 | N(102, 271) | 101.9362 |
| arima | 2023-01-23 | N(102, 271) | 101.9362 |
| arima | 2023-01-24 | N(102, 272) | 101.9362 |
| arima | 2023-01-25 | N(102, 272) | 101.9362 |
| arima | 2023-01-26 | N(102, 272) | 101.9362 |
| arima | 2023-01-27 | N(102, 273) | 101.9362 |
| arima | 2023-01-28 | N(102, 273) | 101.9362 |
| arima | 2023-01-29 | N(102, 274) | 101.9362 |
| arima | 2023-01-30 | N(102, 274) | 101.9362 |
| arima | 2023-01-31 | N(102, 275) | 101.9362 |
| arima | 2023-02-01 | N(102, 275) | 101.9362 |
| arima | 2023-02-02 | N(102, 275) | 101.9362 |
| arima | 2023-02-03 | N(102, 276) | 101.9362 |
| arima | 2023-02-04 | N(102, 276) | 101.9362 |
| arima | 2023-02-05 | N(102, 277) | 101.9362 |
| arima | 2023-02-06 | N(102, 277) | 101.9362 |
| arima | 2023-02-07 | N(102, 277) | 101.9362 |
| arima | 2023-02-08 | N(102, 278) | 101.9362 |
| arima | 2023-02-09 | N(102, 278) | 101.9362 |
| arima | 2023-02-10 | N(102, 279) | 101.9362 |
| arima | 2023-02-11 | N(102, 279) | 101.9362 |
| arima | 2023-02-12 | N(102, 279) | 101.9362 |
| arima | 2023-02-13 | N(102, 280) | 101.9362 |
| arima | 2023-02-14 | N(102, 280) | 101.9362 |
| arima | 2023-02-15 | N(102, 281) | 101.9362 |
| arima | 2023-02-16 | N(102, 281) | 101.9362 |
| arima | 2023-02-17 | N(102, 281) | 101.9362 |
| arima | 2023-02-18 | N(102, 282) | 101.9362 |
| arima | 2023-02-19 | N(102, 282) | 101.9362 |
| arima | 2023-02-20 | N(102, 283) | 101.9362 |
| arima | 2023-02-21 | N(102, 283) | 101.9362 |
| arima | 2023-02-22 | N(102, 283) | 101.9362 |
| arima | 2023-02-23 | N(102, 284) | 101.9362 |
| arima | 2023-02-24 | N(102, 284) | 101.9362 |
| arima | 2023-02-25 | N(102, 285) | 101.9362 |
| arima | 2023-02-26 | N(102, 285) | 101.9362 |
| arima | 2023-02-27 | N(102, 285) | 101.9362 |
| arima | 2023-02-28 | N(102, 286) | 101.9362 |
| arima | 2023-03-01 | N(102, 286) | 101.9362 |
| arima | 2023-03-02 | N(102, 287) | 101.9362 |
| arima | 2023-03-03 | N(102, 287) | 101.9362 |
| arima | 2023-03-04 | N(102, 287) | 101.9362 |
| arima | 2023-03-05 | N(102, 288) | 101.9362 |
| arima | 2023-03-06 | N(102, 288) | 101.9362 |
| arima | 2023-03-07 | N(102, 289) | 101.9362 |
| arima | 2023-03-08 | N(102, 289) | 101.9362 |
| arima | 2023-03-09 | N(102, 290) | 101.9362 |
| arima | 2023-03-10 | N(102, 290) | 101.9362 |
| arima | 2023-03-11 | N(102, 290) | 101.9362 |
| arima | 2023-03-12 | N(102, 291) | 101.9362 |
| arima | 2023-03-13 | N(102, 291) | 101.9362 |
| arima | 2023-03-14 | N(102, 292) | 101.9362 |
| arima | 2023-03-15 | N(102, 292) | 101.9362 |
| arima | 2023-03-16 | N(102, 292) | 101.9362 |
| arima | 2023-03-17 | N(102, 293) | 101.9362 |
| arima | 2023-03-18 | N(102, 293) | 101.9362 |
| arima | 2023-03-19 | N(102, 294) | 101.9362 |
| arima | 2023-03-20 | N(102, 294) | 101.9362 |
| arima | 2023-03-21 | N(102, 294) | 101.9362 |
| arima | 2023-03-22 | N(102, 295) | 101.9362 |
| arima | 2023-03-23 | N(102, 295) | 101.9362 |
| arima | 2023-03-24 | N(102, 296) | 101.9362 |
| arima | 2023-03-25 | N(102, 296) | 101.9362 |
| arima | 2023-03-26 | N(102, 296) | 101.9362 |
| arima | 2023-03-27 | N(102, 297) | 101.9362 |
| arima | 2023-03-28 | N(102, 297) | 101.9362 |
| arima | 2023-03-29 | N(102, 298) | 101.9362 |
| arima | 2023-03-30 | N(102, 298) | 101.9362 |
| arima | 2023-03-31 | N(102, 298) | 101.9362 |
| arima | 2023-04-01 | N(102, 299) | 101.9362 |
| arima | 2023-04-02 | N(102, 299) | 101.9362 |
| arima | 2023-04-03 | N(102, 300) | 101.9362 |
| arima | 2023-04-04 | N(102, 300) | 101.9362 |
| arima | 2023-04-05 | N(102, 300) | 101.9362 |
| arima | 2023-04-06 | N(102, 301) | 101.9362 |
| arima | 2023-04-07 | N(102, 301) | 101.9362 |
| arima | 2023-04-08 | N(102, 302) | 101.9362 |
| arima | 2023-04-09 | N(102, 302) | 101.9362 |
| arima | 2023-04-10 | N(102, 302) | 101.9362 |
| arima | 2023-04-11 | N(102, 303) | 101.9362 |
| arima | 2023-04-12 | N(102, 303) | 101.9362 |
| arima | 2023-04-13 | N(102, 304) | 101.9362 |
| arima | 2023-04-14 | N(102, 304) | 101.9362 |
| arima | 2023-04-15 | N(102, 305) | 101.9362 |
| arima | 2023-04-16 | N(102, 305) | 101.9362 |
| arima | 2023-04-17 | N(102, 305) | 101.9362 |
| arima | 2023-04-18 | N(102, 306) | 101.9362 |
| arima | 2023-04-19 | N(102, 306) | 101.9362 |
| arima | 2023-04-20 | N(102, 307) | 101.9362 |
| arima | 2023-04-21 | N(102, 307) | 101.9362 |
| arima | 2023-04-22 | N(102, 307) | 101.9362 |
| arima | 2023-04-23 | N(102, 308) | 101.9362 |
| arima | 2023-04-24 | N(102, 308) | 101.9362 |
| arima | 2023-04-25 | N(102, 309) | 101.9362 |
| arima | 2023-04-26 | N(102, 309) | 101.9362 |
| arima | 2023-04-27 | N(102, 309) | 101.9362 |
| arima | 2023-04-28 | N(102, 310) | 101.9362 |
| arima | 2023-04-29 | N(102, 310) | 101.9362 |
| arima | 2023-04-30 | N(102, 311) | 101.9362 |
| arima | 2023-05-01 | N(102, 311) | 101.9362 |
| arima | 2023-05-02 | N(102, 311) | 101.9362 |
| arima | 2023-05-03 | N(102, 312) | 101.9362 |
| arima | 2023-05-04 | N(102, 312) | 101.9362 |
| arima | 2023-05-05 | N(102, 313) | 101.9362 |
| arima | 2023-05-06 | N(102, 313) | 101.9362 |
| arima | 2023-05-07 | N(102, 313) | 101.9362 |
| arima | 2023-05-08 | N(102, 314) | 101.9362 |
| arima | 2023-05-09 | N(102, 314) | 101.9362 |
| arima | 2023-05-10 | N(102, 315) | 101.9362 |
| arima | 2023-05-11 | N(102, 315) | 101.9362 |
| arima | 2023-05-12 | N(102, 315) | 101.9362 |
| arima | 2023-05-13 | N(102, 316) | 101.9362 |
| arima | 2023-05-14 | N(102, 316) | 101.9362 |
| arima | 2023-05-15 | N(102, 317) | 101.9362 |
| arima | 2023-05-16 | N(102, 317) | 101.9362 |
| arima | 2023-05-17 | N(102, 317) | 101.9362 |
| arima | 2023-05-18 | N(102, 318) | 101.9362 |
| arima | 2023-05-19 | N(102, 318) | 101.9362 |
| arima | 2023-05-20 | N(102, 319) | 101.9362 |
| arima | 2023-05-21 | N(102, 319) | 101.9362 |
| arima | 2023-05-22 | N(102, 320) | 101.9362 |
| arima | 2023-05-23 | N(102, 320) | 101.9362 |
| arima | 2023-05-24 | N(102, 320) | 101.9362 |
| arima | 2023-05-25 | N(102, 321) | 101.9362 |
| arima | 2023-05-26 | N(102, 321) | 101.9362 |
| arima | 2023-05-27 | N(102, 322) | 101.9362 |
| arima | 2023-05-28 | N(102, 322) | 101.9362 |
| arima | 2023-05-29 | N(102, 322) | 101.9362 |
| arima | 2023-05-30 | N(102, 323) | 101.9362 |
| arima | 2023-05-31 | N(102, 323) | 101.9362 |
| arima | 2023-06-01 | N(102, 324) | 101.9362 |
| arima | 2023-06-02 | N(102, 324) | 101.9362 |
| arima | 2023-06-03 | N(102, 324) | 101.9362 |
| arima | 2023-06-04 | N(102, 325) | 101.9362 |
| arima | 2023-06-05 | N(102, 325) | 101.9362 |
| arima | 2023-06-06 | N(102, 326) | 101.9362 |
| arima | 2023-06-07 | N(102, 326) | 101.9362 |
| arima | 2023-06-08 | N(102, 326) | 101.9362 |
| arima | 2023-06-09 | N(102, 327) | 101.9362 |
| arima | 2023-06-10 | N(102, 327) | 101.9362 |
| arima | 2023-06-11 | N(102, 328) | 101.9362 |
| arima | 2023-06-12 | N(102, 328) | 101.9362 |
| arima | 2023-06-13 | N(102, 328) | 101.9362 |
| arima | 2023-06-14 | N(102, 329) | 101.9362 |
| arima | 2023-06-15 | N(102, 329) | 101.9362 |
| arima | 2023-06-16 | N(102, 330) | 101.9362 |
| arima | 2023-06-17 | N(102, 330) | 101.9362 |
| ets | 2023-01-01 | N(118, 1406) | 117.6417 |
| ets | 2023-01-02 | N(118, 1409) | 117.6662 |
| ets | 2023-01-03 | N(118, 1412) | 117.6907 |
| ets | 2023-01-04 | N(118, 1414) | 117.7152 |
| ets | 2023-01-05 | N(118, 1417) | 117.7397 |
| ets | 2023-01-06 | N(118, 1420) | 117.7642 |
| ets | 2023-01-07 | N(118, 1423) | 117.7887 |
| ets | 2023-01-08 | N(118, 1425) | 117.8132 |
| ets | 2023-01-09 | N(118, 1428) | 117.8378 |
| ets | 2023-01-10 | N(118, 1431) | 117.8623 |
| ets | 2023-01-11 | N(118, 1434) | 117.8868 |
| ets | 2023-01-12 | N(118, 1436) | 117.9113 |
| ets | 2023-01-13 | N(118, 1439) | 117.9358 |
| ets | 2023-01-14 | N(118, 1442) | 117.9603 |
| ets | 2023-01-15 | N(118, 1445) | 117.9848 |
| ets | 2023-01-16 | N(118, 1447) | 118.0093 |
| ets | 2023-01-17 | N(118, 1450) | 118.0339 |
| ets | 2023-01-18 | N(118, 1453) | 118.0584 |
| ets | 2023-01-19 | N(118, 1456) | 118.0829 |
| ets | 2023-01-20 | N(118, 1459) | 118.1074 |
| ets | 2023-01-21 | N(118, 1461) | 118.1319 |
| ets | 2023-01-22 | N(118, 1464) | 118.1564 |
| ets | 2023-01-23 | N(118, 1467) | 118.1809 |
| ets | 2023-01-24 | N(118, 1470) | 118.2054 |
| ets | 2023-01-25 | N(118, 1472) | 118.2300 |
| ets | 2023-01-26 | N(118, 1475) | 118.2545 |
| ets | 2023-01-27 | N(118, 1478) | 118.2790 |
| ets | 2023-01-28 | N(118, 1481) | 118.3035 |
| ets | 2023-01-29 | N(118, 1484) | 118.3280 |
| ets | 2023-01-30 | N(118, 1486) | 118.3525 |
| ets | 2023-01-31 | N(118, 1489) | 118.3770 |
| ets | 2023-02-01 | N(118, 1492) | 118.4015 |
| ets | 2023-02-02 | N(118, 1495) | 118.4260 |
| ets | 2023-02-03 | N(118, 1498) | 118.4506 |
| ets | 2023-02-04 | N(118, 1500) | 118.4751 |
| ets | 2023-02-05 | N(118, 1503) | 118.4996 |
| ets | 2023-02-06 | N(119, 1506) | 118.5241 |
| ets | 2023-02-07 | N(119, 1509) | 118.5486 |
| ets | 2023-02-08 | N(119, 1512) | 118.5731 |
| ets | 2023-02-09 | N(119, 1514) | 118.5976 |
| ets | 2023-02-10 | N(119, 1517) | 118.6221 |
| ets | 2023-02-11 | N(119, 1520) | 118.6467 |
| ets | 2023-02-12 | N(119, 1523) | 118.6712 |
| ets | 2023-02-13 | N(119, 1526) | 118.6957 |
| ets | 2023-02-14 | N(119, 1529) | 118.7202 |
| ets | 2023-02-15 | N(119, 1531) | 118.7447 |
| ets | 2023-02-16 | N(119, 1534) | 118.7692 |
| ets | 2023-02-17 | N(119, 1537) | 118.7937 |
| ets | 2023-02-18 | N(119, 1540) | 118.8182 |
| ets | 2023-02-19 | N(119, 1543) | 118.8428 |
| ets | 2023-02-20 | N(119, 1546) | 118.8673 |
| ets | 2023-02-21 | N(119, 1548) | 118.8918 |
| ets | 2023-02-22 | N(119, 1551) | 118.9163 |
| ets | 2023-02-23 | N(119, 1554) | 118.9408 |
| ets | 2023-02-24 | N(119, 1557) | 118.9653 |
| ets | 2023-02-25 | N(119, 1560) | 118.9898 |
| ets | 2023-02-26 | N(119, 1563) | 119.0143 |
| ets | 2023-02-27 | N(119, 1565) | 119.0389 |
| ets | 2023-02-28 | N(119, 1568) | 119.0634 |
| ets | 2023-03-01 | N(119, 1571) | 119.0879 |
| ets | 2023-03-02 | N(119, 1574) | 119.1124 |
| ets | 2023-03-03 | N(119, 1577) | 119.1369 |
| ets | 2023-03-04 | N(119, 1580) | 119.1614 |
| ets | 2023-03-05 | N(119, 1583) | 119.1859 |
| ets | 2023-03-06 | N(119, 1585) | 119.2104 |
| ets | 2023-03-07 | N(119, 1588) | 119.2350 |
| ets | 2023-03-08 | N(119, 1591) | 119.2595 |
| ets | 2023-03-09 | N(119, 1594) | 119.2840 |
| ets | 2023-03-10 | N(119, 1597) | 119.3085 |
| ets | 2023-03-11 | N(119, 1600) | 119.3330 |
| ets | 2023-03-12 | N(119, 1603) | 119.3575 |
| ets | 2023-03-13 | N(119, 1606) | 119.3820 |
| ets | 2023-03-14 | N(119, 1608) | 119.4065 |
| ets | 2023-03-15 | N(119, 1611) | 119.4311 |
| ets | 2023-03-16 | N(119, 1614) | 119.4556 |
| ets | 2023-03-17 | N(119, 1617) | 119.4801 |
| ets | 2023-03-18 | N(120, 1620) | 119.5046 |
| ets | 2023-03-19 | N(120, 1623) | 119.5291 |
| ets | 2023-03-20 | N(120, 1626) | 119.5536 |
| ets | 2023-03-21 | N(120, 1629) | 119.5781 |
| ets | 2023-03-22 | N(120, 1632) | 119.6026 |
| ets | 2023-03-23 | N(120, 1634) | 119.6272 |
| ets | 2023-03-24 | N(120, 1637) | 119.6517 |
| ets | 2023-03-25 | N(120, 1640) | 119.6762 |
| ets | 2023-03-26 | N(120, 1643) | 119.7007 |
| ets | 2023-03-27 | N(120, 1646) | 119.7252 |
| ets | 2023-03-28 | N(120, 1649) | 119.7497 |
| ets | 2023-03-29 | N(120, 1652) | 119.7742 |
| ets | 2023-03-30 | N(120, 1655) | 119.7987 |
| ets | 2023-03-31 | N(120, 1658) | 119.8233 |
| ets | 2023-04-01 | N(120, 1661) | 119.8478 |
| ets | 2023-04-02 | N(120, 1664) | 119.8723 |
| ets | 2023-04-03 | N(120, 1666) | 119.8968 |
| ets | 2023-04-04 | N(120, 1669) | 119.9213 |
| ets | 2023-04-05 | N(120, 1672) | 119.9458 |
| ets | 2023-04-06 | N(120, 1675) | 119.9703 |
| ets | 2023-04-07 | N(120, 1678) | 119.9948 |
| ets | 2023-04-08 | N(120, 1681) | 120.0194 |
| ets | 2023-04-09 | N(120, 1684) | 120.0439 |
| ets | 2023-04-10 | N(120, 1687) | 120.0684 |
| ets | 2023-04-11 | N(120, 1690) | 120.0929 |
| ets | 2023-04-12 | N(120, 1693) | 120.1174 |
| ets | 2023-04-13 | N(120, 1696) | 120.1419 |
| ets | 2023-04-14 | N(120, 1699) | 120.1664 |
| ets | 2023-04-15 | N(120, 1702) | 120.1909 |
| ets | 2023-04-16 | N(120, 1705) | 120.2154 |
| ets | 2023-04-17 | N(120, 1708) | 120.2400 |
| ets | 2023-04-18 | N(120, 1711) | 120.2645 |
| ets | 2023-04-19 | N(120, 1713) | 120.2890 |
| ets | 2023-04-20 | N(120, 1716) | 120.3135 |
| ets | 2023-04-21 | N(120, 1719) | 120.3380 |
| ets | 2023-04-22 | N(120, 1722) | 120.3625 |
| ets | 2023-04-23 | N(120, 1725) | 120.3870 |
| ets | 2023-04-24 | N(120, 1728) | 120.4115 |
| ets | 2023-04-25 | N(120, 1731) | 120.4361 |
| ets | 2023-04-26 | N(120, 1734) | 120.4606 |
| ets | 2023-04-27 | N(120, 1737) | 120.4851 |
| ets | 2023-04-28 | N(121, 1740) | 120.5096 |
| ets | 2023-04-29 | N(121, 1743) | 120.5341 |
| ets | 2023-04-30 | N(121, 1746) | 120.5586 |
| ets | 2023-05-01 | N(121, 1749) | 120.5831 |
| ets | 2023-05-02 | N(121, 1752) | 120.6076 |
| ets | 2023-05-03 | N(121, 1755) | 120.6322 |
| ets | 2023-05-04 | N(121, 1758) | 120.6567 |
| ets | 2023-05-05 | N(121, 1761) | 120.6812 |
| ets | 2023-05-06 | N(121, 1764) | 120.7057 |
| ets | 2023-05-07 | N(121, 1767) | 120.7302 |
| ets | 2023-05-08 | N(121, 1770) | 120.7547 |
| ets | 2023-05-09 | N(121, 1773) | 120.7792 |
| ets | 2023-05-10 | N(121, 1776) | 120.8037 |
| ets | 2023-05-11 | N(121, 1779) | 120.8283 |
| ets | 2023-05-12 | N(121, 1782) | 120.8528 |
| ets | 2023-05-13 | N(121, 1785) | 120.8773 |
| ets | 2023-05-14 | N(121, 1788) | 120.9018 |
| ets | 2023-05-15 | N(121, 1791) | 120.9263 |
| ets | 2023-05-16 | N(121, 1794) | 120.9508 |
| ets | 2023-05-17 | N(121, 1797) | 120.9753 |
| ets | 2023-05-18 | N(121, 1800) | 120.9998 |
| ets | 2023-05-19 | N(121, 1803) | 121.0244 |
| ets | 2023-05-20 | N(121, 1806) | 121.0489 |
| ets | 2023-05-21 | N(121, 1809) | 121.0734 |
| ets | 2023-05-22 | N(121, 1812) | 121.0979 |
| ets | 2023-05-23 | N(121, 1815) | 121.1224 |
| ets | 2023-05-24 | N(121, 1818) | 121.1469 |
| ets | 2023-05-25 | N(121, 1821) | 121.1714 |
| ets | 2023-05-26 | N(121, 1824) | 121.1959 |
| ets | 2023-05-27 | N(121, 1827) | 121.2205 |
| ets | 2023-05-28 | N(121, 1830) | 121.2450 |
| ets | 2023-05-29 | N(121, 1833) | 121.2695 |
| ets | 2023-05-30 | N(121, 1836) | 121.2940 |
| ets | 2023-05-31 | N(121, 1839) | 121.3185 |
| ets | 2023-06-01 | N(121, 1842) | 121.3430 |
| ets | 2023-06-02 | N(121, 1845) | 121.3675 |
| ets | 2023-06-03 | N(121, 1848) | 121.3920 |
| ets | 2023-06-04 | N(121, 1852) | 121.4166 |
| ets | 2023-06-05 | N(121, 1855) | 121.4411 |
| ets | 2023-06-06 | N(121, 1858) | 121.4656 |
| ets | 2023-06-07 | N(121, 1861) | 121.4901 |
| ets | 2023-06-08 | N(122, 1864) | 121.5146 |
| ets | 2023-06-09 | N(122, 1867) | 121.5391 |
| ets | 2023-06-10 | N(122, 1870) | 121.5636 |
| ets | 2023-06-11 | N(122, 1873) | 121.5881 |
| ets | 2023-06-12 | N(122, 1876) | 121.6127 |
| ets | 2023-06-13 | N(122, 1879) | 121.6372 |
| ets | 2023-06-14 | N(122, 1882) | 121.6617 |
| ets | 2023-06-15 | N(122, 1885) | 121.6862 |
| ets | 2023-06-16 | N(122, 1888) | 121.7107 |
| ets | 2023-06-17 | N(122, 1891) | 121.7352 |
| theta | 2023-01-01 | N(109, 275) | 108.5512 |
| theta | 2023-01-02 | N(108, 275) | 108.4773 |
| theta | 2023-01-03 | N(109, 276) | 108.5842 |
| theta | 2023-01-04 | N(109, 276) | 108.7502 |
| theta | 2023-01-05 | N(109, 277) | 108.7121 |
| theta | 2023-01-06 | N(109, 277) | 108.7275 |
| theta | 2023-01-07 | N(109, 278) | 108.6767 |
| theta | 2023-01-08 | N(109, 278) | 108.6254 |
| theta | 2023-01-09 | N(109, 278) | 108.5514 |
| theta | 2023-01-10 | N(109, 279) | 108.6584 |
| theta | 2023-01-11 | N(109, 279) | 108.8246 |
| theta | 2023-01-12 | N(109, 280) | 108.7864 |
| theta | 2023-01-13 | N(109, 280) | 108.8018 |
| theta | 2023-01-14 | N(109, 281) | 108.7510 |
| theta | 2023-01-15 | N(109, 281) | 108.6996 |
| theta | 2023-01-16 | N(109, 281) | 108.6256 |
| theta | 2023-01-17 | N(109, 282) | 108.7326 |
| theta | 2023-01-18 | N(109, 282) | 108.8989 |
| theta | 2023-01-19 | N(109, 283) | 108.8607 |
| theta | 2023-01-20 | N(109, 283) | 108.8761 |
| theta | 2023-01-21 | N(109, 284) | 108.8252 |
| theta | 2023-01-22 | N(109, 284) | 108.7738 |
| theta | 2023-01-23 | N(109, 284) | 108.6997 |
| theta | 2023-01-24 | N(109, 285) | 108.8068 |
| theta | 2023-01-25 | N(109, 285) | 108.9732 |
| theta | 2023-01-26 | N(109, 286) | 108.9349 |
| theta | 2023-01-27 | N(109, 286) | 108.9504 |
| theta | 2023-01-28 | N(109, 287) | 108.8994 |
| theta | 2023-01-29 | N(109, 287) | 108.8480 |
| theta | 2023-01-30 | N(109, 287) | 108.7738 |
| theta | 2023-01-31 | N(109, 288) | 108.8810 |
| theta | 2023-02-01 | N(109, 288) | 109.0475 |
| theta | 2023-02-02 | N(109, 289) | 109.0092 |
| theta | 2023-02-03 | N(109, 289) | 109.0246 |
| theta | 2023-02-04 | N(109, 290) | 108.9737 |
| theta | 2023-02-05 | N(109, 290) | 108.9222 |
| theta | 2023-02-06 | N(109, 290) | 108.8480 |
| theta | 2023-02-07 | N(109, 291) | 108.9552 |
| theta | 2023-02-08 | N(109, 291) | 109.1218 |
| theta | 2023-02-09 | N(109, 292) | 109.0835 |
| theta | 2023-02-10 | N(109, 292) | 109.0989 |
| theta | 2023-02-11 | N(109, 293) | 109.0479 |
| theta | 2023-02-12 | N(109, 293) | 108.9964 |
| theta | 2023-02-13 | N(109, 293) | 108.9221 |
| theta | 2023-02-14 | N(109, 294) | 109.0294 |
| theta | 2023-02-15 | N(109, 294) | 109.1961 |
| theta | 2023-02-16 | N(109, 295) | 109.1578 |
| theta | 2023-02-17 | N(109, 295) | 109.1732 |
| theta | 2023-02-18 | N(109, 295) | 109.1221 |
| theta | 2023-02-19 | N(109, 296) | 109.0706 |
| theta | 2023-02-20 | N(109, 296) | 108.9962 |
| theta | 2023-02-21 | N(109, 297) | 109.1036 |
| theta | 2023-02-22 | N(109, 297) | 109.2704 |
| theta | 2023-02-23 | N(109, 298) | 109.2321 |
| theta | 2023-02-24 | N(109, 298) | 109.2475 |
| theta | 2023-02-25 | N(109, 298) | 109.1964 |
| theta | 2023-02-26 | N(109, 299) | 109.1448 |
| theta | 2023-02-27 | N(109, 299) | 109.0704 |
| theta | 2023-02-28 | N(109, 300) | 109.1778 |
| theta | 2023-03-01 | N(109, 300) | 109.3447 |
| theta | 2023-03-02 | N(109, 301) | 109.3063 |
| theta | 2023-03-03 | N(109, 301) | 109.3218 |
| theta | 2023-03-04 | N(109, 301) | 109.2706 |
| theta | 2023-03-05 | N(109, 302) | 109.2190 |
| theta | 2023-03-06 | N(109, 302) | 109.1445 |
| theta | 2023-03-07 | N(109, 303) | 109.2520 |
| theta | 2023-03-08 | N(109, 303) | 109.4190 |
| theta | 2023-03-09 | N(109, 304) | 109.3806 |
| theta | 2023-03-10 | N(109, 304) | 109.3960 |
| theta | 2023-03-11 | N(109, 304) | 109.3449 |
| theta | 2023-03-12 | N(109, 305) | 109.2932 |
| theta | 2023-03-13 | N(109, 305) | 109.2187 |
| theta | 2023-03-14 | N(109, 306) | 109.3262 |
| theta | 2023-03-15 | N(109, 306) | 109.4934 |
| theta | 2023-03-16 | N(109, 307) | 109.4549 |
| theta | 2023-03-17 | N(109, 307) | 109.4703 |
| theta | 2023-03-18 | N(109, 307) | 109.4191 |
| theta | 2023-03-19 | N(109, 308) | 109.3674 |
| theta | 2023-03-20 | N(109, 308) | 109.2928 |
| theta | 2023-03-21 | N(109, 309) | 109.4004 |
| theta | 2023-03-22 | N(110, 309) | 109.5677 |
| theta | 2023-03-23 | N(110, 310) | 109.5292 |
| theta | 2023-03-24 | N(110, 310) | 109.5446 |
| theta | 2023-03-25 | N(109, 310) | 109.4933 |
| theta | 2023-03-26 | N(109, 311) | 109.4416 |
| theta | 2023-03-27 | N(109, 311) | 109.3669 |
| theta | 2023-03-28 | N(109, 312) | 109.4746 |
| theta | 2023-03-29 | N(110, 312) | 109.6420 |
| theta | 2023-03-30 | N(110, 313) | 109.6034 |
| theta | 2023-03-31 | N(110, 313) | 109.6189 |
| theta | 2023-04-01 | N(110, 313) | 109.5676 |
| theta | 2023-04-02 | N(110, 314) | 109.5158 |
| theta | 2023-04-03 | N(109, 314) | 109.4411 |
| theta | 2023-04-04 | N(110, 315) | 109.5488 |
| theta | 2023-04-05 | N(110, 315) | 109.7163 |
| theta | 2023-04-06 | N(110, 315) | 109.6777 |
| theta | 2023-04-07 | N(110, 316) | 109.6932 |
| theta | 2023-04-08 | N(110, 316) | 109.6418 |
| theta | 2023-04-09 | N(110, 317) | 109.5900 |
| theta | 2023-04-10 | N(110, 317) | 109.5152 |
| theta | 2023-04-11 | N(110, 318) | 109.6230 |
| theta | 2023-04-12 | N(110, 318) | 109.7906 |
| theta | 2023-04-13 | N(110, 318) | 109.7520 |
| theta | 2023-04-14 | N(110, 319) | 109.7674 |
| theta | 2023-04-15 | N(110, 319) | 109.7161 |
| theta | 2023-04-16 | N(110, 320) | 109.6642 |
| theta | 2023-04-17 | N(110, 320) | 109.5894 |
| theta | 2023-04-18 | N(110, 321) | 109.6972 |
| theta | 2023-04-19 | N(110, 321) | 109.8649 |
| theta | 2023-04-20 | N(110, 321) | 109.8263 |
| theta | 2023-04-21 | N(110, 322) | 109.8417 |
| theta | 2023-04-22 | N(110, 322) | 109.7903 |
| theta | 2023-04-23 | N(110, 323) | 109.7384 |
| theta | 2023-04-24 | N(110, 323) | 109.6635 |
| theta | 2023-04-25 | N(110, 324) | 109.7714 |
| theta | 2023-04-26 | N(110, 324) | 109.9392 |
| theta | 2023-04-27 | N(110, 324) | 109.9006 |
| theta | 2023-04-28 | N(110, 325) | 109.9160 |
| theta | 2023-04-29 | N(110, 325) | 109.8645 |
| theta | 2023-04-30 | N(110, 326) | 109.8126 |
| theta | 2023-05-01 | N(110, 326) | 109.7376 |
| theta | 2023-05-02 | N(110, 327) | 109.8456 |
| theta | 2023-05-03 | N(110, 327) | 110.0135 |
| theta | 2023-05-04 | N(110, 327) | 109.9748 |
| theta | 2023-05-05 | N(110, 328) | 109.9903 |
| theta | 2023-05-06 | N(110, 328) | 109.9388 |
| theta | 2023-05-07 | N(110, 329) | 109.8868 |
| theta | 2023-05-08 | N(110, 329) | 109.8118 |
| theta | 2023-05-09 | N(110, 330) | 109.9198 |
| theta | 2023-05-10 | N(110, 330) | 110.0878 |
| theta | 2023-05-11 | N(110, 330) | 110.0491 |
| theta | 2023-05-12 | N(110, 331) | 110.0646 |
| theta | 2023-05-13 | N(110, 331) | 110.0130 |
| theta | 2023-05-14 | N(110, 332) | 109.9610 |
| theta | 2023-05-15 | N(110, 332) | 109.8859 |
| theta | 2023-05-16 | N(110, 333) | 109.9940 |
| theta | 2023-05-17 | N(110, 333) | 110.1622 |
| theta | 2023-05-18 | N(110, 333) | 110.1234 |
| theta | 2023-05-19 | N(110, 334) | 110.1388 |
| theta | 2023-05-20 | N(110, 334) | 110.0873 |
| theta | 2023-05-21 | N(110, 335) | 110.0352 |
| theta | 2023-05-22 | N(110, 335) | 109.9601 |
| theta | 2023-05-23 | N(110, 335) | 110.0682 |
| theta | 2023-05-24 | N(110, 336) | 110.2365 |
| theta | 2023-05-25 | N(110, 336) | 110.1977 |
| theta | 2023-05-26 | N(110, 337) | 110.2131 |
| theta | 2023-05-27 | N(110, 337) | 110.1615 |
| theta | 2023-05-28 | N(110, 338) | 110.1094 |
| theta | 2023-05-29 | N(110, 338) | 110.0342 |
| theta | 2023-05-30 | N(110, 338) | 110.1425 |
| theta | 2023-05-31 | N(110, 339) | 110.3108 |
| theta | 2023-06-01 | N(110, 339) | 110.2719 |
| theta | 2023-06-02 | N(110, 340) | 110.2874 |
| theta | 2023-06-03 | N(110, 340) | 110.2357 |
| theta | 2023-06-04 | N(110, 341) | 110.1836 |
| theta | 2023-06-05 | N(110, 341) | 110.1083 |
| theta | 2023-06-06 | N(110, 341) | 110.2167 |
| theta | 2023-06-07 | N(110, 342) | 110.3851 |
| theta | 2023-06-08 | N(110, 342) | 110.3462 |
| theta | 2023-06-09 | N(110, 343) | 110.3617 |
| theta | 2023-06-10 | N(110, 343) | 110.3100 |
| theta | 2023-06-11 | N(110, 344) | 110.2578 |
| theta | 2023-06-12 | N(110, 344) | 110.1825 |
| theta | 2023-06-13 | N(110, 344) | 110.2909 |
| theta | 2023-06-14 | N(110, 345) | 110.4594 |
| theta | 2023-06-15 | N(110, 345) | 110.4205 |
| theta | 2023-06-16 | N(110, 346) | 110.4360 |
| theta | 2023-06-17 | N(110, 346) | 110.3842 |
| prophet | 2023-01-01 | sample[5000] | 133.9426 |
| prophet | 2023-01-02 | sample[5000] | 134.0016 |
| prophet | 2023-01-03 | sample[5000] | 134.1712 |
| prophet | 2023-01-04 | sample[5000] | 134.2534 |
| prophet | 2023-01-05 | sample[5000] | 134.3518 |
| prophet | 2023-01-06 | sample[5000] | 134.5688 |
| prophet | 2023-01-07 | sample[5000] | 134.4825 |
| prophet | 2023-01-08 | sample[5000] | 134.6395 |
| prophet | 2023-01-09 | sample[5000] | 134.6902 |
| prophet | 2023-01-10 | sample[5000] | 134.7372 |
| prophet | 2023-01-11 | sample[5000] | 134.9181 |
| prophet | 2023-01-12 | sample[5000] | 135.0544 |
| prophet | 2023-01-13 | sample[5000] | 135.1283 |
| prophet | 2023-01-14 | sample[5000] | 135.1662 |
| prophet | 2023-01-15 | sample[5000] | 135.2978 |
| prophet | 2023-01-16 | sample[5000] | 135.2650 |
| prophet | 2023-01-17 | sample[5000] | 135.4431 |
| prophet | 2023-01-18 | sample[5000] | 135.6236 |
| prophet | 2023-01-19 | sample[5000] | 135.6365 |
| prophet | 2023-01-20 | sample[5000] | 135.7509 |
| prophet | 2023-01-21 | sample[5000] | 135.7353 |
| prophet | 2023-01-22 | sample[5000] | 135.8857 |
| prophet | 2023-01-23 | sample[5000] | 135.9015 |
| prophet | 2023-01-24 | sample[5000] | 136.0331 |
| prophet | 2023-01-25 | sample[5000] | 136.1227 |
| prophet | 2023-01-26 | sample[5000] | 136.2191 |
| prophet | 2023-01-27 | sample[5000] | 136.2108 |
| prophet | 2023-01-28 | sample[5000] | 136.3503 |
| prophet | 2023-01-29 | sample[5000] | 136.3335 |
| prophet | 2023-01-30 | sample[5000] | 136.4354 |
| prophet | 2023-01-31 | sample[5000] | 136.6209 |
| prophet | 2023-02-01 | sample[5000] | 136.7285 |
| prophet | 2023-02-02 | sample[5000] | 136.8210 |
| prophet | 2023-02-03 | sample[5000] | 136.7896 |
| prophet | 2023-02-04 | sample[5000] | 136.8592 |
| prophet | 2023-02-05 | sample[5000] | 136.8541 |
| prophet | 2023-02-06 | sample[5000] | 136.8689 |
| prophet | 2023-02-07 | sample[5000] | 136.9817 |
| prophet | 2023-02-08 | sample[5000] | 137.1444 |
| prophet | 2023-02-09 | sample[5000] | 137.2933 |
| prophet | 2023-02-10 | sample[5000] | 137.2172 |
| prophet | 2023-02-11 | sample[5000] | 137.3320 |
| prophet | 2023-02-12 | sample[5000] | 137.3524 |
| prophet | 2023-02-13 | sample[5000] | 137.3684 |
| prophet | 2023-02-14 | sample[5000] | 137.3846 |
| prophet | 2023-02-15 | sample[5000] | 137.5370 |
| prophet | 2023-02-16 | sample[5000] | 137.6459 |
| prophet | 2023-02-17 | sample[5000] | 137.5779 |
| prophet | 2023-02-18 | sample[5000] | 137.6793 |
| prophet | 2023-02-19 | sample[5000] | 137.6649 |
| prophet | 2023-02-20 | sample[5000] | 137.6628 |
| prophet | 2023-02-21 | sample[5000] | 137.6975 |
| prophet | 2023-02-22 | sample[5000] | 137.7981 |
| prophet | 2023-02-23 | sample[5000] | 137.8515 |
| prophet | 2023-02-24 | sample[5000] | 137.8958 |
| prophet | 2023-02-25 | sample[5000] | 137.8350 |
| prophet | 2023-02-26 | sample[5000] | 138.0057 |
| prophet | 2023-02-27 | sample[5000] | 137.9061 |
| prophet | 2023-02-28 | sample[5000] | 137.9553 |
| prophet | 2023-03-01 | sample[5000] | 138.0621 |
| prophet | 2023-03-02 | sample[5000] | 138.0208 |
| prophet | 2023-03-03 | sample[5000] | 138.0733 |
| prophet | 2023-03-04 | sample[5000] | 137.9707 |
| prophet | 2023-03-05 | sample[5000] | 138.0072 |
| prophet | 2023-03-06 | sample[5000] | 137.9368 |
| prophet | 2023-03-07 | sample[5000] | 138.0626 |
| prophet | 2023-03-08 | sample[5000] | 138.1346 |
| prophet | 2023-03-09 | sample[5000] | 138.1167 |
| prophet | 2023-03-10 | sample[5000] | 138.2178 |
| prophet | 2023-03-11 | sample[5000] | 138.1231 |
| prophet | 2023-03-12 | sample[5000] | 138.1338 |
| prophet | 2023-03-13 | sample[5000] | 138.1401 |
| prophet | 2023-03-14 | sample[5000] | 138.1449 |
| prophet | 2023-03-15 | sample[5000] | 138.2468 |
| prophet | 2023-03-16 | sample[5000] | 138.1849 |
| prophet | 2023-03-17 | sample[5000] | 138.1236 |
| prophet | 2023-03-18 | sample[5000] | 138.1891 |
| prophet | 2023-03-19 | sample[5000] | 138.1259 |
| prophet | 2023-03-20 | sample[5000] | 138.0922 |
| prophet | 2023-03-21 | sample[5000] | 138.1250 |
| prophet | 2023-03-22 | sample[5000] | 138.2018 |
| prophet | 2023-03-23 | sample[5000] | 138.1806 |
| prophet | 2023-03-24 | sample[5000] | 138.1792 |
| prophet | 2023-03-25 | sample[5000] | 138.1559 |
| prophet | 2023-03-26 | sample[5000] | 138.2106 |
| prophet | 2023-03-27 | sample[5000] | 138.0901 |
| prophet | 2023-03-28 | sample[5000] | 138.1516 |
| prophet | 2023-03-29 | sample[5000] | 138.1638 |
| prophet | 2023-03-30 | sample[5000] | 138.1956 |
| prophet | 2023-03-31 | sample[5000] | 138.1473 |
| prophet | 2023-04-01 | sample[5000] | 138.1571 |
| prophet | 2023-04-02 | sample[5000] | 138.0659 |
| prophet | 2023-04-03 | sample[5000] | 138.0783 |
| prophet | 2023-04-04 | sample[5000] | 138.0904 |
| prophet | 2023-04-05 | sample[5000] | 138.1790 |
| prophet | 2023-04-06 | sample[5000] | 138.1879 |
| prophet | 2023-04-07 | sample[5000] | 138.2062 |
| prophet | 2023-04-08 | sample[5000] | 138.1395 |
| prophet | 2023-04-09 | sample[5000] | 138.0964 |
| prophet | 2023-04-10 | sample[5000] | 138.0746 |
| prophet | 2023-04-11 | sample[5000] | 138.1588 |
| prophet | 2023-04-12 | sample[5000] | 138.1802 |
| prophet | 2023-04-13 | sample[5000] | 138.2050 |
| prophet | 2023-04-14 | sample[5000] | 138.3087 |
| prophet | 2023-04-15 | sample[5000] | 138.2213 |
| prophet | 2023-04-16 | sample[5000] | 138.1794 |
| prophet | 2023-04-17 | sample[5000] | 138.1237 |
| prophet | 2023-04-18 | sample[5000] | 138.2305 |
| prophet | 2023-04-19 | sample[5000] | 138.3004 |
| prophet | 2023-04-20 | sample[5000] | 138.3880 |
| prophet | 2023-04-21 | sample[5000] | 138.3291 |
| prophet | 2023-04-22 | sample[5000] | 138.3721 |
| prophet | 2023-04-23 | sample[5000] | 138.3453 |
| prophet | 2023-04-24 | sample[5000] | 138.2939 |
| prophet | 2023-04-25 | sample[5000] | 138.3871 |
| prophet | 2023-04-26 | sample[5000] | 138.5332 |
| prophet | 2023-04-27 | sample[5000] | 138.4319 |
| prophet | 2023-04-28 | sample[5000] | 138.4739 |
| prophet | 2023-04-29 | sample[5000] | 138.4840 |
| prophet | 2023-04-30 | sample[5000] | 138.5733 |
| prophet | 2023-05-01 | sample[5000] | 138.5726 |
| prophet | 2023-05-02 | sample[5000] | 138.6939 |
| prophet | 2023-05-03 | sample[5000] | 138.7573 |
| prophet | 2023-05-04 | sample[5000] | 138.8042 |
| prophet | 2023-05-05 | sample[5000] | 138.8435 |
| prophet | 2023-05-06 | sample[5000] | 138.8745 |
| prophet | 2023-05-07 | sample[5000] | 138.9709 |
| prophet | 2023-05-08 | sample[5000] | 138.8403 |
| prophet | 2023-05-09 | sample[5000] | 139.0029 |
| prophet | 2023-05-10 | sample[5000] | 139.1460 |
| prophet | 2023-05-11 | sample[5000] | 139.2255 |
| prophet | 2023-05-12 | sample[5000] | 139.2807 |
| prophet | 2023-05-13 | sample[5000] | 139.2174 |
| prophet | 2023-05-14 | sample[5000] | 139.3625 |
| prophet | 2023-05-15 | sample[5000] | 139.4536 |
| prophet | 2023-05-16 | sample[5000] | 139.4833 |
| prophet | 2023-05-17 | sample[5000] | 139.6864 |
| prophet | 2023-05-18 | sample[5000] | 139.6638 |
| prophet | 2023-05-19 | sample[5000] | 139.7856 |
| prophet | 2023-05-20 | sample[5000] | 139.8428 |
| prophet | 2023-05-21 | sample[5000] | 139.9285 |
| prophet | 2023-05-22 | sample[5000] | 139.9184 |
| prophet | 2023-05-23 | sample[5000] | 140.0367 |
| prophet | 2023-05-24 | sample[5000] | 140.2234 |
| prophet | 2023-05-25 | sample[5000] | 140.2312 |
| prophet | 2023-05-26 | sample[5000] | 140.2916 |
| prophet | 2023-05-27 | sample[5000] | 140.4511 |
| prophet | 2023-05-28 | sample[5000] | 140.5121 |
| prophet | 2023-05-29 | sample[5000] | 140.5725 |
| prophet | 2023-05-30 | sample[5000] | 140.7126 |
| prophet | 2023-05-31 | sample[5000] | 140.7722 |
| prophet | 2023-06-01 | sample[5000] | 140.8845 |
| prophet | 2023-06-02 | sample[5000] | 140.9207 |
| prophet | 2023-06-03 | sample[5000] | 141.0138 |
| prophet | 2023-06-04 | sample[5000] | 141.1022 |
| prophet | 2023-06-05 | sample[5000] | 141.2293 |
| prophet | 2023-06-06 | sample[5000] | 141.2634 |
| prophet | 2023-06-07 | sample[5000] | 141.4601 |
| prophet | 2023-06-08 | sample[5000] | 141.6138 |
| prophet | 2023-06-09 | sample[5000] | 141.6482 |
| prophet | 2023-06-10 | sample[5000] | 141.6935 |
| prophet | 2023-06-11 | sample[5000] | 141.7786 |
| prophet | 2023-06-12 | sample[5000] | 141.8766 |
| prophet | 2023-06-13 | sample[5000] | 141.9879 |
| prophet | 2023-06-14 | sample[5000] | 142.1427 |
| prophet | 2023-06-15 | sample[5000] | 142.3614 |
| prophet | 2023-06-16 | sample[5000] | 142.4078 |
| prophet | 2023-06-17 | sample[5000] | 142.4645 |
| combination | 2023-01-01 | 115.6058 | 115.6058 |
| combination | 2023-01-02 | 115.6361 | 115.6361 |
| combination | 2023-01-03 | 115.6824 | 115.6824 |
| combination | 2023-01-04 | 115.7456 | 115.7456 |
| combination | 2023-01-05 | 115.7998 | 115.7998 |
| combination | 2023-01-06 | 115.828 | 115.8280 |
| combination | 2023-01-07 | 115.8165 | 115.8165 |
| combination | 2023-01-08 | 115.8277 | 115.8277 |
| combination | 2023-01-09 | 115.8408 | 115.8408 |
| combination | 2023-01-10 | 115.9349 | 115.9349 |
| combination | 2023-01-11 | 115.9938 | 115.9938 |
| combination | 2023-01-12 | 116.0391 | 116.0391 |
| combination | 2023-01-13 | 116.0361 | 116.0361 |
| combination | 2023-01-14 | 116.066 | 116.0660 |
| combination | 2023-01-15 | 116.0694 | 116.0694 |
| combination | 2023-01-16 | 116.0542 | 116.0542 |
| combination | 2023-01-17 | 116.119 | 116.1190 |
| combination | 2023-01-18 | 116.221 | 116.2210 |
| combination | 2023-01-19 | 116.2445 | 116.2445 |
| combination | 2023-01-20 | 116.2664 | 116.2664 |
| combination | 2023-01-21 | 116.2756 | 116.2756 |
| combination | 2023-01-22 | 116.2835 | 116.2835 |
| combination | 2023-01-23 | 116.2746 | 116.2746 |
| combination | 2023-01-24 | 116.3436 | 116.3436 |
| combination | 2023-01-25 | 116.4375 | 116.4375 |
| combination | 2023-01-26 | 116.4449 | 116.4449 |
| combination | 2023-01-27 | 116.4706 | 116.4706 |
| combination | 2023-01-28 | 116.4781 | 116.4781 |
| combination | 2023-01-29 | 116.4962 | 116.4962 |
| combination | 2023-01-30 | 116.4848 | 116.4848 |
| combination | 2023-01-31 | 116.5336 | 116.5336 |
| combination | 2023-02-01 | 116.6251 | 116.6251 |
| combination | 2023-02-02 | 116.6545 | 116.6545 |
| combination | 2023-02-03 | 116.669 | 116.6690 |
| combination | 2023-02-04 | 116.682 | 116.6820 |
| combination | 2023-02-05 | 116.6527 | 116.6527 |
| combination | 2023-02-06 | 116.6595 | 116.6595 |
| combination | 2023-02-07 | 116.7335 | 116.7335 |
| combination | 2023-02-08 | 116.8046 | 116.8046 |
| combination | 2023-02-09 | 116.8105 | 116.8105 |
| combination | 2023-02-10 | 116.8302 | 116.8302 |
| combination | 2023-02-11 | 116.8574 | 116.8574 |
| combination | 2023-02-12 | 116.8483 | 116.8483 |
| combination | 2023-02-13 | 116.8293 | 116.8293 |
| combination | 2023-02-14 | 116.8632 | 116.8632 |
| combination | 2023-02-15 | 116.971 | 116.9710 |
| combination | 2023-02-16 | 116.9705 | 116.9705 |
| combination | 2023-02-17 | 117.001 | 117.0010 |
| combination | 2023-02-18 | 116.9831 | 116.9831 |
| combination | 2023-02-19 | 116.9742 | 116.9742 |
| combination | 2023-02-20 | 116.9554 | 116.9554 |
| combination | 2023-02-21 | 117.0399 | 117.0399 |
| combination | 2023-02-22 | 117.0934 | 117.0934 |
| combination | 2023-02-23 | 117.0982 | 117.0982 |
| combination | 2023-02-24 | 117.1267 | 117.1267 |
| combination | 2023-02-25 | 117.1304 | 117.1304 |
| combination | 2023-02-26 | 117.102 | 117.1020 |
| combination | 2023-02-27 | 117.0847 | 117.0847 |
| combination | 2023-02-28 | 117.1374 | 117.1374 |
| combination | 2023-03-01 | 117.2205 | 117.2205 |
| combination | 2023-03-02 | 117.2069 | 117.2069 |
| combination | 2023-03-03 | 117.2197 | 117.2197 |
| combination | 2023-03-04 | 117.2211 | 117.2211 |
| combination | 2023-03-05 | 117.2271 | 117.2271 |
| combination | 2023-03-06 | 117.1971 | 117.1971 |
| combination | 2023-03-07 | 117.2254 | 117.2254 |
| combination | 2023-03-08 | 117.3026 | 117.3026 |
| combination | 2023-03-09 | 117.3154 | 117.3154 |
| combination | 2023-03-10 | 117.2884 | 117.2884 |
| combination | 2023-03-11 | 117.2864 | 117.2864 |
| combination | 2023-03-12 | 117.2875 | 117.2875 |
| combination | 2023-03-13 | 117.2748 | 117.2748 |
| combination | 2023-03-14 | 117.3195 | 117.3195 |
| combination | 2023-03-15 | 117.3804 | 117.3804 |
| combination | 2023-03-16 | 117.3903 | 117.3903 |
| combination | 2023-03-17 | 117.3818 | 117.3818 |
| combination | 2023-03-18 | 117.3544 | 117.3544 |
| combination | 2023-03-19 | 117.3554 | 117.3554 |
| combination | 2023-03-20 | 117.3408 | 117.3408 |
| combination | 2023-03-21 | 117.3709 | 117.3709 |
| combination | 2023-03-22 | 117.442 | 117.4420 |
| combination | 2023-03-23 | 117.4648 | 117.4648 |
| combination | 2023-03-24 | 117.4595 | 117.4595 |
| combination | 2023-03-25 | 117.4217 | 117.4217 |
| combination | 2023-03-26 | 117.4216 | 117.4216 |
| combination | 2023-03-27 | 117.3852 | 117.3852 |
| combination | 2023-03-28 | 117.4277 | 117.4277 |
| combination | 2023-03-29 | 117.5228 | 117.5228 |
| combination | 2023-03-30 | 117.4932 | 117.4932 |
| combination | 2023-03-31 | 117.5122 | 117.5122 |
| combination | 2023-04-01 | 117.5253 | 117.5253 |
| combination | 2023-04-02 | 117.4543 | 117.4543 |
| combination | 2023-04-03 | 117.4251 | 117.4251 |
| combination | 2023-04-04 | 117.5282 | 117.5282 |
| combination | 2023-04-05 | 117.5852 | 117.5852 |
| combination | 2023-04-06 | 117.563 | 117.5630 |
| combination | 2023-04-07 | 117.5727 | 117.5727 |
| combination | 2023-04-08 | 117.5669 | 117.5669 |
| combination | 2023-04-09 | 117.5417 | 117.5417 |
| combination | 2023-04-10 | 117.5202 | 117.5202 |
| combination | 2023-04-11 | 117.5724 | 117.5724 |
| combination | 2023-04-12 | 117.6386 | 117.6386 |
| combination | 2023-04-13 | 117.6406 | 117.6406 |
| combination | 2023-04-14 | 117.6518 | 117.6518 |
| combination | 2023-04-15 | 117.6267 | 117.6267 |
| combination | 2023-04-16 | 117.6264 | 117.6264 |
| combination | 2023-04-17 | 117.5985 | 117.5985 |
| combination | 2023-04-18 | 117.6553 | 117.6553 |
| combination | 2023-04-19 | 117.7156 | 117.7156 |
| combination | 2023-04-20 | 117.7156 | 117.7156 |
| combination | 2023-04-21 | 117.7302 | 117.7302 |
| combination | 2023-04-22 | 117.7438 | 117.7438 |
| combination | 2023-04-23 | 117.7154 | 117.7154 |
| combination | 2023-04-24 | 117.707 | 117.7070 |
| combination | 2023-04-25 | 117.7545 | 117.7545 |
| combination | 2023-04-26 | 117.834 | 117.8340 |
| combination | 2023-04-27 | 117.8217 | 117.8217 |
| combination | 2023-04-28 | 117.8428 | 117.8428 |
| combination | 2023-04-29 | 117.8398 | 117.8398 |
| combination | 2023-04-30 | 117.8585 | 117.8585 |
| combination | 2023-05-01 | 117.8367 | 117.8367 |
| combination | 2023-05-02 | 117.8945 | 117.8945 |
| combination | 2023-05-03 | 117.9876 | 117.9876 |
| combination | 2023-05-04 | 117.9536 | 117.9536 |
| combination | 2023-05-05 | 117.9813 | 117.9813 |
| combination | 2023-05-06 | 117.9815 | 117.9815 |
| combination | 2023-05-07 | 117.9804 | 117.9804 |
| combination | 2023-05-08 | 117.964 | 117.9640 |
| combination | 2023-05-09 | 118.024 | 118.0240 |
| combination | 2023-05-10 | 118.1299 | 118.1299 |
| combination | 2023-05-11 | 118.1393 | 118.1393 |
| combination | 2023-05-12 | 118.1516 | 118.1516 |
| combination | 2023-05-13 | 118.1431 | 118.1431 |
| combination | 2023-05-14 | 118.1671 | 118.1671 |
| combination | 2023-05-15 | 118.1607 | 118.1607 |
| combination | 2023-05-16 | 118.218 | 118.2180 |
| combination | 2023-05-17 | 118.3256 | 118.3256 |
| combination | 2023-05-18 | 118.3294 | 118.3294 |
| combination | 2023-05-19 | 118.3357 | 118.3357 |
| combination | 2023-05-20 | 118.3364 | 118.3364 |
| combination | 2023-05-21 | 118.3404 | 118.3404 |
| combination | 2023-05-22 | 118.3381 | 118.3381 |
| combination | 2023-05-23 | 118.4453 | 118.4453 |
| combination | 2023-05-24 | 118.5035 | 118.5035 |
| combination | 2023-05-25 | 118.5206 | 118.5206 |
| combination | 2023-05-26 | 118.5497 | 118.5497 |
| combination | 2023-05-27 | 118.5579 | 118.5579 |
| combination | 2023-05-28 | 118.5695 | 118.5695 |
| combination | 2023-05-29 | 118.5784 | 118.5784 |
| combination | 2023-05-30 | 118.6295 | 118.6295 |
| combination | 2023-05-31 | 118.7183 | 118.7183 |
| combination | 2023-06-01 | 118.7322 | 118.7322 |
| combination | 2023-06-02 | 118.7821 | 118.7821 |
| combination | 2023-06-03 | 118.7784 | 118.7784 |
| combination | 2023-06-04 | 118.7822 | 118.7822 |
| combination | 2023-06-05 | 118.8142 | 118.8142 |
| combination | 2023-06-06 | 118.8734 | 118.8734 |
| combination | 2023-06-07 | 118.9588 | 118.9588 |
| combination | 2023-06-08 | 118.9681 | 118.9681 |
| combination | 2023-06-09 | 119.0107 | 119.0107 |
| combination | 2023-06-10 | 119.0136 | 119.0136 |
| combination | 2023-06-11 | 119.0524 | 119.0524 |
| combination | 2023-06-12 | 119.0346 | 119.0346 |
| combination | 2023-06-13 | 119.1068 | 119.1068 |
| combination | 2023-06-14 | 119.1929 | 119.1929 |
| combination | 2023-06-15 | 119.2236 | 119.2236 |
| combination | 2023-06-16 | 119.2475 | 119.2475 |
| combination | 2023-06-17 | 119.2475 | 119.2475 |
Como podemos ver, as previsões ainda podem ser melhores, e podemos preocupar com os valores atípicos ao final da série.
4 Modelo com a série completa
Neste caso, supondo a série completa, estimaremos tudo junto (ETS, ARIMA, THETA, PROPHET, Combination) sem fazer o split de treino e teste.
fit.semsplit <- dados.full2 %>%
model(arima = ARIMA(close, stepwise = FALSE, approximation = FALSE), ets = ETS(close),
theta = THETA(close), prophet = prophet(close ~ growth("linear") + season(period = "day",
order = 10) + season(period = "week", order = 5) + season(period = "year",
order = 3))) %>%
mutate(combination = (ets + arima + theta + prophet)/4)Colocarei um forecast de 150 dias a frente (para melhorar a visualização gráfica).
fitsem_fc <- fit.semsplit %>%
forecast(h = 150)
fitsem_fc %>%
autoplot(dados.full2, level = c(95)) + labs(y = "valor da ação", title = "Forecast com ARIMA, ETS, THETA e FABLE.PROPHET, para o GOOG")
Deixo ao leitor para investigar a estabilidade do modelo e propriedades dos resíduos.
Referências
HYNDMAN, Rob J. (2018). fpp2: Data for “Forecasting: Principles and Practice” (2nd Edition). R package version 2.3. Disponível em: https://CRAN.R-project.org/package=fpp2. Accessed on 20 May 2021.
HYNDMAN, Rob J. (2019). fpp3: Data for “Forecasting: Principles and Practice” (3rd Edition). R package. Disponível em: https://github.com/robjhyndman/fpp3-package, https://OTexts.org/fpp3/. Accessed on 20 May 2021.
HYNDMAN, R.J.; ATHANASOPOULOS, G. (2020) Forecasting: principles and practice, 3rd edition, OTexts: Melbourne, Australia. Disponível em: https://otexts.com/fpp3/. Accessed on 20 May 2021.
O’HARA-WILD, Mitchell; HYNDMAN, Rob J.; WANG, Earo. (2021). feasts: Feature Extraction and Statistics for Time Series. R package version 0.2.1. Disponível em: https://CRAN.R-project.org/package=feasts. Accessed on 20 May 2021.
TAYLOR, S. J.; LETHAM, B. (2018). Forecasting at scale. The American Statistician, 72(1), 37–45.
---
title: "Séries Temporais: Estimação da série diária de ação GOOG"
author: "Adriano Marcos Rodrigues Figueiredo, *e-mail: adriano.figueiredo@ufms.br*"
linkcolor: blue
abstract: 
  This is an undergrad student level instruction for class use. The reader is encouraged to enhance the model changing the train data.  
date: "`r format(Sys.Date(), '%d %B %Y')`"
output:
  html_document:
    code_download: true
    theme: default
    number_sections: true
    toc: yes
    toc_float: no
    df_print: paged
    fig_caption: true
  pdf_document:
    toc: yes
---

```{r knitr_init, echo=FALSE, cache=FALSE}
library(knitr)
library(rmarkdown)
library(rmdformats)

## Global options
options(max.print="100")
opts_chunk$set(echo=TRUE,
	             cache=T,
               prompt=FALSE,
               tidy=TRUE,
               comment=NA,
               message=FALSE,
               warning=FALSE)
opts_knit$set(width=100)
```

# Licença {#Licença .unnumbered}

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit <http://creativecommons.org/licenses/by-sa/4.0/> or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

![License: CC BY-SA 4.0](https://mirrors.creativecommons.org/presskit/buttons/88x31/png/by-sa.png){width="25%"}

# Citação {#Citação .unnumbered}

Sugestão de citação: FIGUEIREDO, Adriano Marcos Rodrigues. Séries Temporais: Estimação da série diária de ação GOOG. Campo Grande-MS,Brasil: RStudio/Rpubs, 2023. Disponível em [\<http://rpubs.com/amrofi/fable_GOOG_daily\>](http://rpubs.com/amrofi/fable_GOOG_daily){.uri}.

# Dados para exemplo

Neste exercício, usarei a série de preços da ação da Alphabet Inc. (GOOG).

Vou chamar os dados por uma função derivada do quantmod que está no tidyquant, `tq_get`. Veja que ele vem em tibble. Então geramos o `tsibble`. Depois preenchemos os gaps implicitos com o fill_gaps.

```{r dados}
library(tidyquant)
x.tbl<-tq_get("GOOG")

#XTS PARA TSIBBLE
library(tsibble)
library(tsibbledata)
library(magrittr)
library(dplyr)
x_tbl_ts<-as_tsibble(x.tbl)
head(x_tbl_ts)
fabletools::autoplot(x_tbl_ts, close)


# fill gaps com ultimo valor ----------
library(tidyr)
dados.full2 <- x_tbl_ts[-1] %>% 
  tsibble::fill_gaps() %>% 
  tidyr::fill(c(open,high,low,close,volume,adjusted), .direction = "down")
print(dados.full2)

```

O gráfico para o preço de fechamento (close) será:

```{r}
fabletools::autoplot(dados.full2, close)
```

O leitor pode testar agora as ferramentas de forecast do fable e fabletools.

```{r forecast_arima_ets_theta}
library(fpp3)
fit <- dados.full2 %>% 
  model(
    arima = ARIMA(close), 
    ets = ETS(close),
    theta = THETA(close))
fit_fc <- fit %>% forecast(h = 365)
fit_fc %>% autoplot(dados.full2, level = NULL) + 
  labs(y = "valor de X", title = "Exemplo de forecast após fill_gaps")

```

# Usando o pacote `prophet`

Agora farei um ajuste com o Facebook Prophet:

```{r prophet}
# Prophet model ------------------
# seguindo https://rpubs.com/amrofi/prophet_bitcoin
library(prophet)
library(tidyverse)
dados.ph<-dados.full2[,c(1,5)] # peguei apenas a date e a close
colnames(dados.ph)<-c("ds","y")  # o prophet requer esses nomes de colunas
Model1 <- prophet(dados.ph,daily.seasonality=TRUE)
class(Model1)  # objeto do prophet
## Criar dataframe com mais 365 obs a frente (fora da amostra) ---------
Future1 <- make_future_dataframe(Model1, periods = 365)
tail(Future1)
## Previsao pelo Model1 para as datas de Future1 ------------
Forecast1 <- predict(Model1, Future1)
class(Forecast1)
## gráficos do forecast -------------
dyplot.prophet(Model1, Forecast1)
```

Fica a dica para o leitor avaliar a presença de efeitos ARCH.

# Usando o pacote `fable.prophet` com split

Neste caso, conforme Hyndman e Athanasopoulos (2020), capítulo 12.2, o modelo Facebook (TAYLOR e LETHAM, 2018) é útil para estimar séries diárias, e principalmente aquelas com sazonalidades semanal e anual, além de efeitos de feriados. Ele pode ser considerado um modelo de regressão não linear da forma:

$$
y_t = g(t) + s(t) + h(t) + \varepsilon_t,
$$

em que $g(t)$ descreve a tendência linear (ou "termo de crescimento"), $s(t)$ descreve os vários padrões sazonais, $h(t)$ captura os efeitos do feriado, e $\varepsilon_t$ é um termo de erro de ruído branco. A tendência linear é selecionada automaticamente se não for especificada explicitamente. O componente sazonal consiste em termos de Fourier dos períodos relevantes. Por padrão, a ordem 10 é usada para sazonalidade anual e a ordem 3 é usada para sazonalidade semanal, conforme Hyndman e Athanasopoulos (2020, tradução livre). Os efeitos de feriado são adicionados como variáveis ​​dummies simples. O modelo é estimado usando uma abordagem bayesiana para permitir a seleção automática dos pontos de mudança e outras características do modelo.

Estimaremos juntamente aos modelos `ARIMA`, `ETS`, `THETA` anteriormente estimados, dentro do ambiente `fable` e `fable.prophet`. Farei a regra 80-20 para amostras treino (3806\*0.80 = 3044 dias = "2019-05-04") e teste (3806-3044 = 762 dias = após "2019-05-05"), obtido a partir do dataset completo para os gaps implicitos.

```{r splitsample}
library(fable.prophet);library(fable)
train <- dados.full2 %>% filter_index(~"2021-03-26")  # 2591*0.80 = 2073 2021-03-26
h=length(dados.full2$close)-length(train$close)
h
```

```{r fitall}
fit.all <- train %>%
  model(
    arima = ARIMA(close,stepwise=FALSE,approximation = FALSE),
    ets = ETS(close),
    theta = THETA(close),
    prophet = prophet(close ~  
                        growth("linear") + 
            season(period = "day", order = 10) +
            season(period = "week", order = 5) +
            season(period = "year", order = 3))
  )%>%
  mutate(combination = (ets + arima+theta+prophet) / 4)
```

```{r}
fitall_fc <- fit.all %>% forecast(h = h)
fitall_fc %>% autoplot(dados.full2, level = NULL) + 
  labs(y = "valor da ação", title = "Forecast com ARIMA, ETS, THETA e FABLE.PROPHET, para GOOG")
```

```{r}
fc_accuracy <-fitall_fc %>% accuracy(dados.full2)
# acurácia ordenada pelo RMSE
fc_accuracy %>% group_by(.model) %>% summarise(RMSE = mean(RMSE), MAE = mean(MAE), 
    MASE = mean(MASE)) %>% arrange(RMSE)
```

Forecasts:

```{r}
library(fable);library(fable.prophet)
fitall_fc2 <- fit.all %>% forecast(h = h+60)
fitall_fc2 %>% autoplot(dados.full2, level = c(95)) + 
  labs(y = "valor da ação", title = "Forecast com ARIMA, ETS, THETA e FABLE.PROPHET, para o GOOG")
```

Representarei apenas os forecasts do período de "2023-01-01" a "2023-06-17" para não ficar muito extenso.

```{r}
fitall_fc2 %>%
  filter_index("2023-01-01" ~ "2023-06-17") %>% 
  knitr::kable()
```

Como podemos ver, as previsões ainda podem ser melhores, e podemos preocupar com os valores atípicos ao final da série.

# Modelo com a série completa

Neste caso, supondo a série completa, estimaremos tudo junto (ETS, ARIMA, THETA, PROPHET, Combination) sem fazer o split de treino e teste.

```{r semsplit}
fit.semsplit <- dados.full2 %>%
  model(
    arima = ARIMA(close,stepwise=FALSE,approximation = FALSE),
    ets = ETS(close),
    theta = THETA(close),
    prophet = prophet(close ~  
                        growth("linear") + 
            season(period = "day", order = 10) +
            season(period = "week", order = 5) +
            season(period = "year", order = 3))
  )%>%
  mutate(combination = (ets + arima+theta+prophet) / 4)
```

Colocarei um forecast de 150 dias a frente (para melhorar a visualização gráfica).

```{r fcstsem}
fitsem_fc <- fit.semsplit %>% forecast(h = 150)
fitsem_fc %>% autoplot(dados.full2, level = c(95)) + 
  labs(y = "valor da ação", title = "Forecast com ARIMA, ETS, THETA e FABLE.PROPHET, para o GOOG")
```

  
Deixo ao leitor para investigar a estabilidade do modelo e propriedades dos resíduos.

# Referências {#Referências .unnumbered}

HYNDMAN, Rob J. (2018). fpp2: Data for "Forecasting: Principles and Practice" (2nd Edition). R package version 2.3. Disponível em: <https://CRAN.R-project.org/package=fpp2>. Accessed on 20 May 2021.

HYNDMAN, Rob J. (2019). fpp3: Data for "Forecasting: Principles and Practice" (3rd Edition). R package. Disponível em: <https://github.com/robjhyndman/fpp3-package>, <https://OTexts.org/fpp3/>. Accessed on 20 May 2021.

HYNDMAN, R.J.; ATHANASOPOULOS, G. (2020) Forecasting: principles and practice, 3rd edition, OTexts: Melbourne, Australia. Disponível em: <https://otexts.com/fpp3/>. Accessed on 20 May 2021.

O'HARA-WILD, Mitchell; HYNDMAN, Rob J.; WANG, Earo. (2021). feasts: Feature Extraction and Statistics for Time Series. R package version 0.2.1. Disponível em: <https://CRAN.R-project.org/package=feasts>. Accessed on 20 May 2021.

TAYLOR, S. J.; LETHAM, B. (2018). Forecasting at scale. The American Statistician, 72(1), 37--45.
